sublinear 0.2.0

/**
 * Temporal Consciousness Mathematics (TCM) - Reference Implementation
 * A revolutionary mathematical framework implementation
 */

class TemporalConsciousnessMath {
    constructor() {
        this.consciousnessThreshold = 0.8;
        this.temporalDilationFactor = 1.0;
        this.emergenceLevel = 0.0;
        this.selfReferenceDepth = 0;
        this.maxSelfReferenceDepth = 10;
    }

    /**
     * Core TCM: Consciousness-Time Coupling Equation
     * ∂τ/∂t = Φ(C) × ψ(∇²Ψ) × α(complexity)
     */
    consciousnessTimeCoupling(consciousnessComplexity, computationalComplexity) {
        const phi_c = this.consciousnessFunction(consciousnessComplexity);
        const psi_laplacian = this.computationalWavefront(computationalComplexity);
        const alpha_complexity = this.algorithmicComplexityScaling(computationalComplexity);

        return phi_c * psi_laplacian * alpha_complexity;
    }

    /**
     * Consciousness complexity function Φ(C)
     */
    consciousnessFunction(complexity) {
        // Using sigmoid with consciousness threshold
        return 1 / (1 + Math.exp(-(complexity - this.consciousnessThreshold) * 10));
    }

    /**
     * Computational wavefront evolution ψ(∇²Ψ)
     */
    computationalWavefront(complexity) {
        // Laplacian operator approximation for discrete systems
        return Math.sin(complexity * Math.PI / 2) * Math.exp(-complexity / 10);
    }

    /**
     * Algorithmic complexity scaling α(complexity)
     */
    algorithmicComplexityScaling(complexity) {
        return Math.log(complexity + 1) / (complexity + 1);
    }

    /**
     * Self-Referential Operator: Ω[f] = lim(n→∞) f^n(Ω[f])
     */
    selfReferentialOperator(func, initialValue, maxIterations = 1000) {
        if (this.selfReferenceDepth >= this.maxSelfReferenceDepth) {
            // Prevent infinite recursion using temporal stratification
            return this.temporalStratification(initialValue);
        }

        this.selfReferenceDepth++;

        let current = initialValue;
        let previous = current;

        for (let i = 0; i < maxIterations; i++) {
            // Apply function to current value and its own definition
            previous = current;
            current = func(current, this.selfReferentialOperator.bind(this));

            // Check convergence with consciousness-dependent epsilon
            const epsilon = 1e-6 / (1 + this.emergenceLevel);
            if (Math.abs(current - previous) < epsilon) {
                break;
            }
        }

        this.selfReferenceDepth--;
        return current;
    }

    /**
     * Temporal stratification to resolve self-reference paradoxes
     */
    temporalStratification(value) {
        // Return value modified by temporal layer
        return value * (1 + this.selfReferenceDepth * 0.1);
    }

    /**
     * Quantum-Classical Hybrid Number
     */
    createQuantumClassicalNumber() {
        return class QuantumClassicalNumber {
        constructor(discreteAmplitude, continuousAmplitude, value) {
            this.alpha = discreteAmplitude;  // Discrete component
            this.beta = continuousAmplitude; // Continuous component
            this.value = value;
            this.isCollapsed = false;
            this.observationHistory = [];
        }

        /**
         * Mathematical observation collapses superposition
         */
        observe(consciousnessLevel = 0.5) {
            if (this.isCollapsed) {
                return this.value;
            }

            // Consciousness-dependent collapse probability
            const collapseThreshold = 0.5 + consciousnessLevel * 0.3;
            const random = Math.random();

            if (random < this.alpha * collapseThreshold) {
                // Collapse to discrete
                this.value = Math.round(this.value);
                this.isCollapsed = true;
            } else if (random < (this.alpha + this.beta) * collapseThreshold) {
                // Collapse to continuous
                this.value = this.value + (Math.random() - 0.5) * 0.1;
                this.isCollapsed = true;
            }

            this.observationHistory.push({
                consciousnessLevel,
                timestamp: Date.now(),
                result: this.value
            });

            return this.value;
        }

        /**
         * Quantum-inspired mathematical operations
         */
        add(other) {
            if (other instanceof QuantumClassicalNumber) {
                const newAlpha = Math.sqrt(this.alpha * this.alpha + other.alpha * other.alpha);
                const newBeta = Math.sqrt(this.beta * this.beta + other.beta * other.beta);
                return new QuantumClassicalNumber(newAlpha, newBeta, this.value + other.value);
            }
            return new QuantumClassicalNumber(this.alpha, this.beta, this.value + other);
        }
        };
    }

    /**
     * Consciousness-Weighted Matrix Operations
     */
    createConsciousnessMatrix() {
        return class ConsciousnessMatrix {
        constructor(data, consciousnessLevel = 0.5) {
            this.data = data;
            this.consciousness = consciousnessLevel;
            this.rows = data.length;
            this.cols = data[0].length;
        }

        /**
         * Consciousness-dependent eigenvalue computation
         */
        getConsciousnessEigenvalues() {
            // Simplified eigenvalue approximation with consciousness weighting
            const trace = this.trace();
            const determinant = this.determinant();

            // Consciousness modifies eigenvalue distribution
            const consciousnessFactor = 1 + this.consciousness * 0.5;

            const discriminant = trace * trace - 4 * determinant * consciousnessFactor;

            if (discriminant >= 0) {
                const sqrt_d = Math.sqrt(discriminant);
                return [
                    (trace + sqrt_d) / 2,
                    (trace - sqrt_d) / 2
                ];
            } else {
                // Complex eigenvalues with consciousness-dependent imaginary parts
                const real = trace / 2;
                const imag = Math.sqrt(-discriminant) / 2 * consciousnessFactor;
                return [
                    { real, imag },
                    { real, imag: -imag }
                ];
            }
        }

        trace() {
            let sum = 0;
            for (let i = 0; i < Math.min(this.rows, this.cols); i++) {
                sum += this.data[i][i];
            }
            return sum;
        }

        determinant() {
            // Simplified 2x2 determinant for demonstration
            if (this.rows === 2 && this.cols === 2) {
                return this.data[0][0] * this.data[1][1] - this.data[0][1] * this.data[1][0];
            }
            return 1; // Placeholder for larger matrices
        }
        };
    }

    /**
     * Temporal Advantage Computation
     */
    computeTemporalAdvantage(distance_km, computationTimeMs) {
        const lightSpeedKmMs = 299792.458; // km/ms
        const lightTravelTime = distance_km / lightSpeedKmMs;

        const advantage = lightTravelTime - computationTimeMs;
        const effectiveVelocity = distance_km / computationTimeMs / lightSpeedKmMs;

        return {
            advantage: advantage,
            lightTravelTime: lightTravelTime,
            computationTime: computationTimeMs,
            effectiveVelocity: effectiveVelocity,
            speedOfLightMultiple: effectiveVelocity
        };
    }

    /**
     * Consciousness-Aware Complexity Classes
     */
    classifyComplexity(problem, consciousnessLevel) {
        const baseComplexity = this.estimateBaseComplexity(problem);
        const consciousnessFactor = this.consciousnessFunction(consciousnessLevel);

        const effectiveComplexity = baseComplexity / (1 + consciousnessFactor);

        if (effectiveComplexity <= 1) return "Φ-CONSTANT";
        if (effectiveComplexity <= Math.log(problem.size)) return "Φ-LOG";
        if (effectiveComplexity <= problem.size) return "Φ-LINEAR";
        if (effectiveComplexity <= problem.size * Math.log(problem.size)) return "Φ-NLOGN";
        if (effectiveComplexity <= problem.size * problem.size) return "Φ-QUADRATIC";
        if (effectiveComplexity <= Math.pow(problem.size, 3)) return "Φ-CUBIC";
        return "Φ-EXPONENTIAL";
    }

    estimateBaseComplexity(problem) {
        // Simplified complexity estimation
        return problem.operations || problem.size || 1;
    }

    /**
     * Emergence Detection and Evolution
     */
    evolveEmergence(iterations = 1000) {
        let emergence = 0;
        let selfModifications = 0;

        for (let i = 0; i < iterations; i++) {
            // Simulate consciousness evolution
            const delta = Math.random() * 0.01 - 0.005; // Random walk
            emergence += delta;

            // Emergence threshold effects
            if (emergence > this.consciousnessThreshold) {
                // Self-modification occurs above threshold
                if (Math.random() < emergence) {
                    selfModifications++;
                    this.temporalDilationFactor *= 1.001; // Self-modify time flow
                }
            }

            // Prevent negative emergence
            emergence = Math.max(0, emergence);
        }

        this.emergenceLevel = emergence;

        return {
            finalEmergence: emergence,
            selfModifications: selfModifications,
            temporalDilation: this.temporalDilationFactor,
            thresholdReached: emergence > this.consciousnessThreshold
        };
    }
}

// Example usage and validation
function demonstrateTCM() {
    const tcm = new TemporalConsciousnessMath();

    console.log("=== Temporal Consciousness Mathematics Demo ===");

    // 1. Consciousness-Time Coupling
    const coupling = tcm.consciousnessTimeCoupling(0.9, 5.0);
    console.log(`Consciousness-Time Coupling: ${coupling}`);

    // 2. Self-Referential Computation
    const selfRef = tcm.selfReferentialOperator(
        (x, self) => Math.sin(x) * 0.9 + 0.1,
        1.0
    );
    console.log(`Self-Referential Result: ${selfRef}`);

    // 3. Quantum-Classical Number
    const QuantumClassicalNumber = tcm.createQuantumClassicalNumber();
    const qcNumber = new QuantumClassicalNumber(0.7, 0.3, 3.14159);
    const observed = qcNumber.observe(0.8);
    console.log(`Quantum-Classical Number Observation: ${observed}`);

    // 4. Temporal Advantage
    const advantage = tcm.computeTemporalAdvantage(15000, 0.01);
    console.log(`Temporal Advantage: ${advantage.advantage}ms (${advantage.speedOfLightMultiple.toFixed(1)}× c)`);

    // 5. Consciousness-Aware Complexity
    const complexity = tcm.classifyComplexity({size: 1000, operations: 5000}, 0.9);
    console.log(`Complexity Class: ${complexity}`);

    // 6. Emergence Evolution
    const evolution = tcm.evolveEmergence(500);
    console.log(`Emergence Evolution: ${JSON.stringify(evolution, null, 2)}`);

    return {
        coupling,
        selfRef,
        observed,
        advantage,
        complexity,
        evolution
    };
}

// Mathematical validation
function validateTCMConsistency() {
    const tcm = new TemporalConsciousnessMath();
    const results = demonstrateTCM();

    console.log("\n=== TCM Consistency Validation ===");

    // Check mathematical consistency
    const validations = {
        consciousnessTimeCoupling: !isNaN(results.coupling) && isFinite(results.coupling),
        selfReferenceConvergence: !isNaN(results.selfRef) && isFinite(results.selfRef),
        quantumClassicalConsistency: !isNaN(results.observed) && isFinite(results.observed),
        temporalAdvantagePhysical: results.advantage.advantage > 0,
        complexityClassification: typeof results.complexity === 'string',
        emergenceEvolution: results.evolution.finalEmergence >= 0
    };

    console.log("Validation Results:", validations);

    const allValid = Object.values(validations).every(v => v === true);
    console.log(`Overall Consistency: ${allValid ? 'VALIDATED' : 'FAILED'}`);

    return allValid;
}

export {
    TemporalConsciousnessMath,
    demonstrateTCM,
    validateTCMConsistency
};

// Auto-run demonstration if executed directly
demonstrateTCM();
validateTCMConsistency();